The invention relates to a digital transmission system comprising a receiver, in which system a trellis-based estimation method with a number of states reduced as a result of feedback of at least one feedback value forms estimates for received symbols by means of an estimated impulse response of a transmission system, a feedback value being determined from at least one estimate.
Furthermore, the invention relates to a receiver and a method of receiving a digital signal.
The subject of the invention is determined for digital transmission systems, for example, digital mobile radio systems such as the GSM system or digital Continuous Phase Modulation (CPM) radio relay systems in which trellis-based estimation methods are used which may be used both for equalizing a transmission channel and for decoding other trellis-coded signals (such as, for example, CPM signals).
When digital transmission takes place over dispersive channels, the transmit signal is distorted and disturbed by noise; in GSM, for example, the distortions are caused by multipath propagation and intersymbol interference of the modulation method. Thus, special measures for recovering the transmitted data from the received signal are necessary in the receiver i.e. an equalization method is to be used. As channel coding is often used for increasing the resistance to noise in digital transmission (for example, convolutional coding in GSM), the data estimated by the equalizer are still to be decoded. It is then advantageous when the decoder is not only supplied with estimates of the coded data, but also with reliability information (also termed Soft-Output information (SO information)) by the equalizer, which information indicates with what reliability the data were decided in trellis-based reduced-state equalization methods, which may also be used for equalizing long impulse responses having moderate complexity, the supplied soft-output information may differ considerably from the actual values, which has a degrading effect on the subsequent decoding.
A Pulse Amplitude Modulation (PAM) transmission over a distorting channel that generates Inter-Symbol Interference (ISI), may be modeled in a discrete-time version in an equivalent low-pass range, as is shown in the left-hand part of FIG. 1. The sampled received signal r(k) occurs as a noise-affected convolution of the PAM transmit sequence a(k) having the channel impulse response h(k), whose length is referenced L: ##EQU1## where n(k) represents the discrete-time noise which is assumed to be white noise and is a given fact prior to the sampling when a whitened matched filter is used as a continuous-time receiver input filter. Depending on the modulation method used, the amplitude coefficients and the channel impulse response are either real or complex.
The optimum equalization method with minimum error probability, Maximum Likelihood Sequence Estimation (MLSE), is known from G.D. Forney, "Maximum likelihood sequence estimation of digital sequences in the presence of intersymbol interference", IEEE Transactions on Information Theory, vol. IT-18, 1972, pp. 363-378. There was more particularly shown here that MLSE may be implemented efficiently with the Viterbi Algorithm (VA). However, for long impulse responses h(k), even the VA is hard to realize, because the trellis diagram which is to be made with the VA has Z=ML.sup.L-1 states per time period with M-stage amplitude coefficients, thus the complexity of VA exponentially increases with the length of the discrete-time impulse response. When the number of subsequent symbols affected by a transmitted symbol becomes too large, more cost-effective, ie reduced-state, equalization methods are to be used because of the limited available computing speed.
Furthermore, it is known that first a pre-equalization, ie shortening, of the channel impulse response is to be made by means of decision feedback equalization (DFE). Then either the DFE itself is to make preliminary threshold decisions, or preliminary hard-decision symbols (a.sub.HDF) of the next Viterbi equalizer are fed to the DFE, which in both cases leads to a noticeable degradation due to error propagation.
Furthermore, the impulse response for each state of the equalizer may be shortened by a state-dependent (private) DFE, instead of a state-independent (common) DFE for all the states. The trellis-based algorithm then provides that only the first part of the impulse response having length R+1, with 1.ltoreq.R+1.ltoreq.L, is equalized. Thus the branch metrics are computed for state transitions in the time interval k from a (reduced) state S.sup.(r) (k)=(a(k-1)a(k-2) . . . a(k-R)) to the (reduced) state S.sup.(r) (k+1)=(a(k)a(k-1) . . . a(k-R+1)) (the coefficients a(k-.mu.) indicate the data assumed in the specific state) with the aid of contents of path registers of the respective states. The registers contain hard-decision estimates a.sub.HDF (k-.mu.,S.sup.(r) (k)), R+1.ltoreq..mu..ltoreq.L-1 of the previous data symbols in the path leading to the state S.sup.(r) (k), which estimates are to be updated in each time period. Thus the branch metric becomes ##EQU2## where h(.mu.), O.ltoreq..mu..ltoreq.L-1 which indicate the channel impulse response estimates available to the receiver.
This reduced-state estimation method will be referenced Decision-Feedback Sequence Estimation (DFSE) hereinafter. The states and transitions are no longer assigned unambiguously to a special combination of symbols in the channel memory, but there are henceforth ambiguities, as generally occurs in reduced-state methods, while particularly with DFSE the oldest symbols in the channel memory are taken into account only for preliminary-decision symbol values.
The efficiency of DFSE may be further improved by an upstream all-pass filter which transforms the impulse response into its minimum-phase equivalent. This transformation provides a concentration of the energy of the impulse response in the front part, while the discrete-time noise remains white noise as before. This property of the minimum phase total impulse response motivates an additional reduction of the complexity of the DFSE, in that only h(R+1), h(R+2), . . . , h(R'), R&lt;R'&lt;L-1 are taken into account by private DFEs a.sub.HDF (k-.mu.,S.sup.(r) (k))), but the remaining part of the impulse response h(R'+1), . . . H(L-1) only by a single common DFE a.sub.HDF (k-.mu.,k)). If the last part of the impulse response contains only a small part of the total energy, the omission of the individual state relation (of the private DFEs) hardly reduces the efficiency of the estimation.
These methods produce only hard-decision estimates for the received symbols, without further information about with which certainty the individual decisions were made, ie how likely they are true. This soft-output (SO) information, referenced .sub.m (k) here (the vector .sub.m (k) has a degree of probability for all the transmit symbols a(k)), however, is necessary in many transmission systems for an additionally available channel coding to enhance the resistance to noise, as, in consequence, the results of the decoding can be considerably improved by this SO information after the equalization.
For determining the symbol probabilities .sub.m (k) in block-oriented transmission, particularly an algorithm with a bidirectional recursion rule can be used. First a forward recursion is used for computing the probabilities .alpha.(k,S(k)) for the states S(k).di-elect cons.{1,2, . . . ,Z} at step k, while the received signals considered thus far up to instant k-1 are taken into account. Then, a backward recursion is used for computing probabilities .beta.(k,S(k)) for the received signals considered from the block end back to the step k with a presupposed state S(k) in the real step k. The state probabilities .psi.(k,S(k)) for the states S(k) at step k are then the result of EQU .psi.(k,S(k))=.alpha.(k,S(k)).multidot..beta.(k,S(k)). (3)
while the total received sequence is taken into account.
Since a finite-length impulse response channel generating ISI may always be interpreted as a trellis coder with a FIR structure, the a-posteriori probabilities of the input symbols are the direct result of the state probabilities. Since the bidirectional algorithm also works on the basis of a trellis, it may be a reduced-state one in similar manner to the Viterbi algorithm. For the forward recursion, for computing the .alpha.(k,S.sup.(r) (k)), each of the M.sup.R reduced states is assigned a path register for computing a metric, which path register may be updated in each time period. Two path metrics are stored and used once again for the backward recursion.
For the computation of the symbol probabilities .sub.m (k) in a continuous transmission without block limits formed by trellis-terminated symbols, only a forward recursion, that is, unidirectional recursion, is used contrary to the bidirectional algorithm. Then, similarly to the bidirectional algorithm, state probabilities .alpha.(k,S(k)) are computed. Since, finally, probabilities for the symbols a(k-D) are to be determined while the received signal is known up to instant k, a second recursion is necessary for determining state-related symbol probabilities ##EQU3## With the results of the two recursions, the desired a-posteriori probabilities ##EQU4## can be determined. A state reduction may also be effected with the unidirectional algorithm. By forming overlapping blocks on the receiving side, the bidirectional algorithm may also be used for a continuous transmission. As a result of its smaller complexity, bidirectional algorithm is typically more suitable than the unidirectional algorithm.
For all the known trellis-based reduced-state equalization methods together, the fact is that the quality of the soft-output information .sub.m (k) for a received symbol with a strong state reduction with hard-decision feedback values is insufficient.